Backstepping Control for a Quadrotor Helicopter

This paper presents a nonlinear dynamic model for a quadrotor helicopter in a form suited for backstepping control design. Due to the under-actuated property of quadrotor helicopter, the controller can set the helicopter track three Cartesian positions (x,y,z) and the yaw angle to their desired values and stabilize the pitch and roll angles. The system has been presented into three interconnected subsystems. The first one representing the under-actuated subsystem, gives the dynamic relation of the horizontal positions (x,y) with the pitch and roll angles. The second fully-actuated subsystem gives the dynamics of the vertical position z and the yaw angle. The last subsystem gives the dynamics of the propeller forces. A backstepping control is presented to stabilize the whole system. The design methodology is based on the Lyapunov stability theory. Various simulations of the model show that the control law stabilizes a quadrotor with good tracking